Unsworth's attempt to reassure staff came after what she described as the "tumultuous and very sad" events of the past few days.

She took over as temporary BBC News director on Monday after Helen Boaden was made to step aside pending the outcome of an internal inquiry into Newsnight's axed Jimmy Savile investigation.

She said in the memo: "We now need to restore some equilibrium to the organisation.

"It would be helpful if some of our problems were not played out publicly across social media and in the pages of the national press. We need a collective and collegiate sense of all pulling together to restore trust in the BBC's news output."

Several of the BBC's most prominent journalists – including political editor Nick Robinson, business editor Robert Peston, and the BBC News channel's chief political correspondent Norman Smith – have reported vigorously on the BBC's shortcomings over the course of the Newsnight crisis.

In the memo, Unsworth confirmed that Adrian Van Klaveren had returned to Salford as controller of BBC Radio 5 Live. Van Klaveren was one of the senior editorial executives who oversaw the disastrous Newsnight broadcast on 2 November which made a false allegation about child abuse in north Wales, leading to the resignation of director general George Entwistle on Saturday.

She also stressed that the new BBC News senior line-up – which has so far seen three executives stepping aside from their jobs until the inquiries are concluded – was a temporary one.

Unsworth praised Boaden and the deputy head of news, Stephen Mitchell, who also stepped aside on Monday, and added: "This is a tough time for everyone in the organisation – in particular for those of us in BBC News. And, of course, for some individuals most of all. Both Helen and Steve are outstanding leaders of BBC News whose experience and ability will be much missed in the coming weeks. Many of you have today shown a great deal of support for them and they wanted me to let you know how grateful they are for that."

Sarah Ward Lilley, the deputy head of newsgathering, will temporarily replace Unsworth as head of newsgathering. Jasmin Buttar, the deputy editor of Radio 4's Today programme, will become acting editor after Ceri Thomas became acting deputy director of news.

Karen O'Connor was appointed acting editor of Newsnight on Monday, in place of Liz Gibbons.

Unsworth said: "Ceri, Karen and I do not undertake our new duties lightly. We would rather events had not worked out this way, but with our colleagues on the news group board, we will collectively do our very best to lead the division through these difficult times. We are relying on the support of all of you to achieve this."

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